1. Field of the Invention
The present invention relates to a method for excitation of free torsional vibrations in a spring cantilever, which is clamped in on one side and has a longitudinal extension, of an atomic force microscope (AFM).
2. Description of the Prior Art
The development of the AFM has led to great achievements in the field of surface property examination, particularly in the characterization of surface properties. For the first time, it has became possible to obtain information about surfaces and close-to-the-surface regions of very diverse samples with nanometer resolution, even for magnitudes of single atoms. With the aid of the friction microscope developed from the atomic force microscope or the lateral force microscope, it became possible for the first time to examine one of the oldest phenomena in technology on this scale, friction.
DE 43 24 983 C2 describes an acoustic microscope which operates on the technological basis of an atomic force microscope and is able to measure the elasticity properties of the surface sample. The atomic force microscope has a spring cantilever designed as a leaf spring, usually having a length of between 100 μm and 500 μm, at the one end of which is attached a pyramid-shaped measuring tip having a tip curvature radius of about 50 nanometers is attached.
In order to measure and detect the whole sample surface, the surface of the sample is scanned by the spring cantilever and the measuring tip connected thereto with the aid of a suitable movement device in such a manner that the measuring tip comes in contact with the sample surface at each single scanning point with a given pressure. The degree that the spring cantilever bends can be determined with the aid of an optical sensor unit thereby permitting detection of the topographical excursion of the measuring tip. The optical sensor unit usually provides a laser diode from which is emitted a laser beam directed at the spring cantilever, is reflected at the spring cantilever and is detected by a position-sensitive photodiode. During scanning, the spring cantilever including the measuring tip actively traces a loop in such a manner that the excursion and the pressure remained constant with which the spring cantilever rests on the surface of a sample surface via the measuring tip. The normal voltage required for the excursion is usually converted into a distance value and, encoded as a color value accordingly plotted in a representation showing the surface topography.
In order to, in addition, determine the elasticity properties of the sample surface, an ultrasonic wave generator is provided, which sets the surface of the sample into oscillations while the measuring tip rests at a scanning point on the sample surface. The oscillation excitation by coupling in ultrasonic waves leads to normal oscillations of the surface of the sample which sets the spring cantilever into high-frequency oscillating bending vibrations along its extension.
Detecting the ultrasound-induced, high-frequency vibration behavior of the spring cantilever permits gaining information about the elasticity properties, in particular in the case of a spring cantilever executing normal vibrations on the compression stiffness of the sample surface. Further details are found in the previously mentioned DE 43 24 983 C2.
In contrast to the aforedescribed resonance measurement with vertical oscillation modulation, that is the to-be-examined sample surface is set into normal oscillations, U.S. Pat. No. 5,804,708 describes an atomic force microscope, although with a similar buildup but oscillation excitation of the to-be-examined sample surface occurs with the aid of a signal generator in such a manner that the sample surface executes oscillations that are oriented lateral to the sample surface, with the oscillations directed, in particular, transverse in relation to the longitudinal extension of the spring cantilever.
Due to the oscillation excitation directed transverse to the longitudinal extension of the spring cantilever, the spring cantilever is set into torsional vibrations via the measuring tip which is in contact with the sample surface, with the measuring tip which is at least at times in contact with the sample surface executing vibrations which are directed in longitudinal direction of the sample surface. The vibrations are directed transverse to the longitudinal extension of the spring cantilever, and are polarized. At the points of reversal of the vibrations, the measuring tip briefly adheres to the sample surface, which is deformed by the shear forces acting laterally on the sample surface, until the measuring tip slips back over the sample surface from this situation, which is described by friction.
The shear deformations formed dependent on the pressure with which the measuring tip rests on the sample surface influence the vibration behavior of the measuring tip and the spring cantilever connected thereto in a manner which characterizes the elasticity properties of the sample surface. In this way it is possible to obtain information about the elasticity properties, in particular about the shear contact stiffness of the sample surface from the vibration behavior, for example from the vibration amplitude, the vibration frequency and/or the vibration frequency phase of the vibrations developing in the form of torsional vibrations along the spring cantilever.
In the dynamic friction microscopy, one must fundamentally differentiate between two types of operation. The simpler type of operation relates to the excitation of the spring cantilever below its vibration resonance. This type of operation is used for detecting friction at high relative velocities between the measuring tip and the sample surface to determine the viscous-elasticity properties of the sample materials. The amplitude and/or the phase shift of the vibration of the spring cantilever in relation to the excitation vibration is recorded and evaluated accordingly.
The other type of operation provides for vibration excitation of the spring cantilever at its vibration resonance. Thus, for instance, the position of the resonance frequency of the torsional vibration of the spring cantilever depends on the friction force acting between the measuring tip and the sample surface. Furthermore, the friction force is influenced by the elasticity properties of the materials of the scanning tip and of the sample.
In the latter type of operation, only the position of the resonance of the spring cantilever is examined, but not the absolute torsional vibration amplitude as in the first case. If the length, width and thickness of the spring cantilever and the length of the measuring tip and the elastic constants of the spring cantilever material and its density are known, the so-called lateral contact stiffness or shear-contact stiffness can be calculated from the torsional resonance frequency.
Similar to the preceding method, the vertical or compression contact stiffness can be determined from the bending resonances of the spring cantilever. Experience has taught that precise determination of compression contact stiffness is not possible via the absolute position of the contact resonance, but rather via its shift in relation to the corresponding freely bending resonance of the one-sidedly clamped-in spring cantilever.
An oscillation element, which is placed on the suspension of the one-sidedly clamped-in spring cantilever and excites the spring cantilever to vertically polarized bending vibrations, can be employed to determine the freely bending resonances. However, it has proven to be useful to carry out excitement via a oscillation element, which is placed under the to-be-examined sample and by means of which the sample surface is set into vertical vibrations. Also see U. Rabe, K. Janser, W. Arnold, Rev. Sci Instrum. 67(1997)3281. Longitudinal waves, which propagate through the air, are generated above the sample due to the normal vibrations of the sample surfaces. The spring cantilever, which is clamped in on one side and is held at a distance from the vibrating surface, is set into bending vibration by the sound waves which begin to resonate at a corresponding excitation frequency, the resonance frequencies of which are exactly measurable.
As in the preceding case of measuring the compression contact stiffness, it is also advantageous for determining the shear contact stiffness not to determine the absolute torsional resonance frequency of the spring cantilever but rather to determine its shift in relationship to the corresponding free torsional resonance. The free resonance can be excited with a shear oscillator element which is placed on the suspension of the one-sidedly clamped-in spring cantilever, as described in an article by S. Nakanao, R. Maeda, K. Yamanaka, Jpn. J. Appl. Phys. 36(1997) 3265.
This approach, however, has a number of drawbacks:
1. The oscillation elements on the suspension of the spring cantilever have to be miniaturized due to the their small volume. The miniaturized oscillation elements cannot be designed for a large frequency band width. Moreover, such type miniaturized elements interfere with the natural resonances, leading to misinterpretation of the contact resonances.2. Due to the cross coupling effects, excitation via the suspension of the spring cantilever also leads to excitation of undesirable bending vibrations of the spring cantilever. Coupled, non-linear modes may also crop up which make analysis more difficult if not impossible.3. Commercially available devices require complicated, time-consuming setting up, thereby increasing costs.